In the situation as shown in figure time period of small vertical oscillation of block will be - (String, springs and pulley are ideal)

Options

A. `2pi cos theta sqrt((m)/(2k))`
B. `2pi sec theta sqrt((m)/(2k))`
C. `2pi sin theta sqrt((m)/(2k))`
D. `2pi cosec theta sqrt((m)/(2k))`

Answer

B

Explanation

In the situtation ………….
Let block is displaced through a small displacement `x` in downward direction and elogation in spring `= x_(1)` then
`x cos theta = x_(1)` ….(1)

Restoring force `F = 2 kx_(1)cos theta`
`F = 2k cos^(2)theta x`
Hence `T = 2pi sqrt((m)/(2k cos^(2)theta))= 2pi sec theta sqrt((m)/(2k))`